The implementation of DSP algorithms in VLSI requires trade-offs between factors such as algorithm performance, silicon area, power consumption, and clock frequency. One parameter that affects all of these factors is the word length, or number of bits, used to represent the data. Where extremely precise computations are required, floating point arithmetic may be needed. However, floating point operations can be impractical for high-speed applications, including digital signal processing (DSP), due to the added hardware, overhead, and processing time they demand.
By contrast, fixed point computations often are used when, such as in digital signal processing, extremely high processing rates are desirable. Typically, the word size used to represent a fixed point value is compact relative to floating point, and fixed point computational devices tend to be of simpler, efficient designs, which permit high-speed operation. Most DSP algorithms achieve satisfactory performance in VLSI using fixed-point arithmetic. Therefore, fixed point computations, particularly in the two's complement binary format, are predominant in DSP applications. However, because fixed point systems can only represent a fixed range of numbers, the internal data precision is reduced. In addition to the increased possibility of overflow during a calculation, fixed point operations tend to have a reduce ability to accurately quantize small numbers. Also, fixed point operations tend to require additional digits to represent the precision of the results of an operation. For example, a fixed point multiplication of two signal values, each having an initial precision of m bits, results in a product having 2 m bits. Because the word length of a subsequent operation, or data path, may be limited to only m bits, some form of precision reduction is needed.
Therefore, rounding is desirable where data processing operations, including those involving, for example, binary- and decimal-based operations, generate an undesirably large number of digits of precision, and some form of precision reduction is needed. Precision reduction in fixed point operations comes at a price. For many DSP systems, performance metrics such as signal-to-noise ratio (SNR) and stability are adversely affected by decreasing internal data precision.
When the precision of a signal value is reduced, the difference between input and output values represents an error that is approximately equal to the part of the input signal that is discarded. In general, the statistics of the error can depend upon how the last bit of the output value is determined. Many DSP components, such as digital filters, can be represented by coefficient values related to a characteristic polynomial equation, which is representative of the component's operating characteristics, e.g. a digital filter's transfer function equation. Because the filter coefficients must be represented by finite length values, the behavior of the filter can be greatly influenced by precision reduction errors.
During the processing of a signal, and as the coefficients are updated, precision reduction can introduce errors roughly equivalent to the value of the dropped digits, or loss bits, thereby generating a precision reduction error signal. Signal processing typically involves numerous, sequential, iterative and recursive computations, during which uncompensated precision reduction errors accumulate, thereby degrading filter performance, possibly to the point of filter instability.
Many DSP applications include VLSI components that extensively employ high-speed computations which are susceptible to precision reduction errors. In widely-used adaptive filters and systems, the associated adaption components can be very sensitive to how data precision is reduced. In some instances, precision reduction errors are merely nuisances with little practical impact. However, in the extreme, precision reduction errors can lead to disastrous outcomes, such as in the documented failure of a defensive missile battery during the 1991 Persian Gulf War, which resulted in many lost lives. Because DSP applications are pervasive in modern life, including for example, communications, health care, transportation, defense, and the like, degraded system performance arising from uncompensated precision reduction errors can be of great import. Whether the application is aircraft navigation, critical-care life support, electronic commerce, or global communications, it is imperative that the DSP infrastructure supporting the application operate in a reliable and robust manner to the greatest extent possible.
What is needed, then, are methods and apparatus that substantially eliminate or offset the precision reduction error.